Question: You're having dinner at a restaurant that serves $5$ kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in $4$ different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil). If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with bow ties, cheese sauce, or both?
Solution: $\text{Probability} = \dfrac{\text{Favorable combinations}}{\text{Total possible combinations}}$ There are $4$ flavor choices and $5$ choices for the type of pasta, so there are $4\times5=20$ total possible combinations. If we pick randomly, all the combinations are equally likely. The red combinations are combinations with bow ties, cheese sauce, or both. There are $8$ favorable combinations. The probability of randomly picking one of those dishes is $8$ out of $20$, or $\dfrac{8}{20}$. We can simplify this fraction to $\dfrac{2}{5}$.